Dynamics of SU(1,1) coherent states driven by a damped harmonic oscillator

Analysis of the effects of nonextensivity for a generalized dissipative system in the SU(1,1) coherent states

The characteristics of nonextensivity for a general quantum dissipative oscillatory system in the SU(1,1) coherent states are investigated using the invariant operator method. We consider a deformed Caldirola-Kanai oscillator represented in terms of a parameter q which is a measure of the degree of nonextensivity. The nonextensivity effects on the parametric evolution of the SU(1,1) coherent states are elucidated. We compare our results with those of previous researches and address the advantage of our methodology which adopts the linear invariant operator. In particular, the nonextensive behaviors associated with the fluctuations of canonical variables and the dissipation of quantum energy are analyzed in detail regarding their dependence on q. The properties of SU(1,1) coherent states that we adopt here can be utilized in quantum-information processes such as cloning, swapping, and teleportation of state information.

Quantum Behavior of a Nonextensive Oscillatory Dissipative System in the Coherent State

We investigate the nonextensivity of a generalized dissipative oscillatory system in the Glauber coherent state. We introduce a parameter q as a measure of the nonextensivity of the system. Considering the characteristic of nonextensivity, the system is described by a deformed Caldirola–Kanai oscillator, which is represented in terms of q. We manage the system by describing the associated Hamiltonian in terms of the harmonic oscillator ladder operators. The time evolutions of the canonical variables, the Hamiltonian expectation value, the quantum energy, and the symmetry-breaking in the evolution of the system, are analyzed in detail regarding their dependence on q, damping factor, and the external driving force. The amplitude of the oscillator is slightly quenched as q becomes large, whereas the amplitude of the canonical momentum is enhanced in response to the growth in q. As q increases, the dissipation of the quantum energy becomes a little faster as a manifestation of the nonextensivity of the system. Our results are compared to the classical results, as well as to those in the previous research performed on the basis of the SU(1,1) coherent states. The coherent states, including the Glauber coherent states, can be convenient resources for carrying information, which is crucial in quantum information processing.

The effects of nonextensivity on quantum dissipation

Nonextensive dynamics for a quantum dissipative system described by a Caldirola-Kanai (CK) Hamiltonian is investigated in SU(1,1) coherent states. To see the effects of nonextensivity, the system is generalized through a modification fulfilled by replacing the ordinary exponential function in the standard CK Hamiltonian with the q-exponential function. We confirmed that the time behavior of the system is somewhat different depending on the value of q which is the degree of nonextensivity. The effects of q on quantum energy dissipation and other parameters are illustrated and discussed in detail.